Question

If 2power X is equals to 3power 2 then find x

Answer 1

Answer:

$\large\boxed{\sf{\dfrac{2 log(3) }{ log(2) }}}$

Step-by-step explanation:

Given an equation such that,

${2}^{x} = {3}^{2}$

To find the value of x,

Take log on both sides, we get,

$= > log( {2}^{x} ) = log( {3}^{2} )$

But, we know that,

• $log( {x}^{m} ) = m log(x)$

Therefore, we will get,

$= > x log(2) = 2 log(3) \\ \\ = > x = \frac{2 log(3) }{ log(2) }$

Hence, the required value of x is $\dfrac{2 log(3) }{ log(2) }$.

Some logarithmic formula:

• $log(xy) = log(x) + log(y)$
• $log( \frac{x}{y} ) = log(x) - log(y)$
• $log(1) = 0$